Risk Calculator

Calculate relative risk (RR), absolute risk reduction (ARR), and number needed to treat (NNT) from event rates in exposed and control groups.

RELATIVE RISK (RR)
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Exposed Risk
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Control Risk
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Abs. Risk Reduction
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NNT
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What Is Relative Risk?

Relative risk (RR) is the ratio of the probability of an event occurring in an exposed group to the probability of it occurring in a control group. It is a fundamental measure in epidemiology and clinical trials for quantifying the strength of association between an exposure and an outcome.

An RR of 1.0 indicates no association between exposure and outcome. An RR greater than 1.0 suggests increased risk with exposure, while an RR less than 1.0 suggests a protective effect. For example, an RR of 2.0 means the exposed group has twice the risk of the control group.

Risk Formulas

Relative Risk (RR) = (a / (a+b)) / (c / (c+d))
Absolute Risk Reduction (ARR) = Control Risk - Exposed Risk
Number Needed to Treat (NNT) = 1 / ARR

Interpreting Results

RR ValueInterpretation
RR = 1.0No difference between groups
RR > 1.0Increased risk in exposed group
RR < 1.0Decreased risk (protective effect)
RR = 2.0Twice the risk
RR = 0.5Half the risk

Worked Examples

Consider a clinical trial where 30 of 200 patients in the treatment group experience an adverse event compared to 50 of 200 in the placebo group. The exposed risk is 30/200 = 0.15 (15%), the control risk is 50/200 = 0.25 (25%). The RR = 0.15/0.25 = 0.60, meaning the treatment reduces risk by 40%. The ARR is 0.25 - 0.15 = 0.10 (10%), and the NNT is 1/0.10 = 10, meaning you need to treat 10 patients to prevent one adverse event.

Frequently Asked Questions

What is the difference between relative risk and odds ratio?

Relative risk compares probabilities directly, while the odds ratio compares odds. For rare events (less than 10% incidence), the OR approximates the RR. For common events, the OR exaggerates the association compared to RR. RR is more intuitive but can only be calculated from cohort studies and clinical trials, not case-control studies.

What does NNT mean in clinical practice?

Number Needed to Treat (NNT) represents how many patients must receive a treatment for one additional patient to benefit compared to the control. Lower NNT values indicate more effective treatments. An NNT of 1 would mean every treated patient benefits, which is ideal but rare in practice.